Finite Group Databasebeta

← #17958658

Subgroups — #17958658

Order 4352.

374 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14544046C211yesmaximal, characteristic
2#14544026C211yesmaximal, characteristic
3#14543727C214yesmaximal
4#14533993C211yesmaximal, characteristic
5#11763830—21no—
6#11763826—21no—
7#11763655—21no—
8#11763655—21no—
9#11763654C2212yes—
10#11763654C2212yes—
11C2×C4×Dic34C2211yescharacteristic
12#11762728—21no—
13#11762728—21no—
14#11762714C412yes—
15#11762705—21no—
16#11762705—21no—
17#11762678C2212yes—
18C4×C4⋊Dic17C411yescharacteristic
19C2×C17×C4⋊Q8C411yescharacteristic
20C22×Q8×C17—21no—
21C22×Dic34C2×C411yescharacteristic
22C17×C4⋊Q8—41no—
23C17×C4⋊Q8—41no—
24C2×C4⋊C4×C17—21no—
25C2×C4⋊C4×C17C2×C412yes—
26C2×C42×C17C2×C411yescharacteristic
27C2×C4⋊Dic17—21no—
28C2×C4⋊Dic17C2311yescharacteristic
29C2×#63225—22no—
30C2×#63225—22no—
31C2×#63225D411yescharacteristic
32C2×#63225D411yescharacteristic
33C2×C4×Dic17C2×C412yes—
34C2×C4×Dic17D411yescharacteristic
35C2×C4×Dic17D411yescharacteristic
36C4×Dic34—41no—
37C4×Dic34—41no—
38C22⋊#3624—22no—
39C22⋊#3624—22no—
40#10587544—41no—
41#10587542—41no—
42C4⋊#3624—41no—
43C4×#3624—41no—
44#10587502—21no—
45#10587502—22no—
46#10587502—22no—
47C2×Q8×C17—42no—
48C2×Q8×C17—82no—
49C22×C4×C17—22no—
50C22×C4×C17C22⋊C411yescharacteristic
51C22×C4×C17C22⋊C411yescharacteristic
52C22×C4×C17C22×C411yescharacteristic
53C22×Dic17—22no—
54C22×Dic17C22⋊C411yescharacteristic
55C22×Dic17C22⋊C411yescharacteristic
56C22×Dic17C2×D411yescharacteristic
57C22×Dic17C2×D411yescharacteristic
58C2×Dic34—22no—
59C2×Dic34—22no—
60C2×Dic34—41no—
61C2×#3624—42no—
62C2×#3624—42no—
63C4⋊C4×C17—42no—
64C4⋊C4×C17—41no—
65C4⋊C4×C17—41no—
66C42×C17—21no—
67C42×C17—21no—
68C4⋊Dic17—24no—
69C4⋊Dic17—41no—
70#63225—41no—
71#63225—41no—
72#63225—82no—
73#63225—82no—
74C4×Dic17—21no—
75C4×Dic17—21no—
76C4×Dic17—21no—
77C4×Dic17—21no—
78C4×Dic17—24no—
79#11574—171nomaximal, Sylow
80C23×C17C2×C22⋊C411yescharacteristic
81Q8×C17—84no—
82C2×C4×C17—21no—
83C2×C4×C17—21no—
84C2×C4×C17—22no—
85C2×C4×C17—21no—
86C2×C4×C17—41no—
87C2×C4×C17—42no—
88C2×C4×C17—42no—
89C2×C4×C17—42no—
90C2×C4×C17#9911yescharacteristic
91C2×C4×C17#9911yescharacteristic
92C2×C4×C17#13112yes—
93C2×Dic17—21no—
94C2×Dic17—21no—
95C2×Dic17—24no—
96C2×Dic17—21no—
97C2×Dic17—21no—
98C2×Dic17—21no—
99C2×Dic17—21no—
100C2×Dic17—21no—
101C2×Dic17—42no—
102C2×Dic17—42no—
103C2×Dic17—41no—
104C2×Dic17—41no—
105C2×Dic17#10112yes—
106Dic34—44no—
107#3624—82no—
108#3624—82no—
109#2567—171no—
110#1467—171no—
111#1461—171no—
112#1325—174no—
113C22×C17—21no—
114C22×C17—21no—
115C22×C17#40811yescharacteristic
116C22×C17C2×#9911yescharacteristic
117C22×C17C2×#10111yescharacteristic
118C4×C17—21no—
119C4×C17—22no—
120C4×C17—41no—
121C4×C17—82no—
122C4×C17#35612yes—
123Dic17—22no—
124Dic17—44no—
125Dic17—41no—
126Dic17—41no—
127Dic17—41no—
128C2×C4⋊Q8#59511yescharacteristic
129C2×C4×Q8—171no—
130#432—341no—
131#431—341no—
132#395—341no—
133#395—341no—
134#391—172no—
135#389—341no—
136#389—341no—
137#384—172no—
138C4×C4⋊C4—171no—
139#324—172no—
140#324—172no—
141#324—341no—
142#324—341no—
143C2×C17—21no—
144C2×C17—21no—
145C2×C17#147211yescharacteristic
146C2×C17#212811yescharacteristic
147C2×C17C2×#35611yescharacteristic
148C22×Q8—21no—
149C22×Q8—171no—
150C4⋊Q8—41no—
151C4⋊Q8—41no—
152C4×Q8—681no—
153C4×Q8—681no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—171no—
156C2×C4⋊C4—171no—
157C2×C4⋊C4—171no—
158C2×C4⋊C4—341no—
159C2×C4⋊C4—342no—
160C2×C4⋊C4—342no—
161C2×C4⋊C4C2×#59512yes—
162C2×C42—171no—
163C2×C42—171no—
164C2×C42—172no—
165C2×C42C2×#59511yescharacteristic
166C4⋊C8—681no—
167C4⋊C8—681no—
168C22⋊C8—342no—
169C22⋊C8—342no—
170#97—681no—
171C4×C8—681no—
172#95—342no—
173#95—342no—
174#95—341no—
175C17#1157411yescharacteristic, complemented, Sylow
176C2×Q8—42no—
177C2×Q8—82no—
178C2×Q8—342no—
179C2×Q8—342no—
180C2×Q8—681no—
181C22×C4—22no—
182C22×C4—171no—
183C22×C4—171no—
184C22×C4—171no—
185C22×C4—171no—
186C22×C4—342no—
187C22×C4C22⋊#59511yescharacteristic
188C22×C4C22⋊#59511yescharacteristic
189C22×C4C22×#59511yescharacteristic
190C2×C8—682no—
191C2×C8—682no—
192C4⋊C4—42no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—344no—
196C4⋊C4—681no—
197C4⋊C4—681no—
198C4⋊C4—681no—
199C4⋊C4—1362no—
200C4⋊C4—1362no—
201C42—21no—
202C42—21no—
203C42—341no—
204C42—341no—
205C42—341no—
206C42—341no—
207C42—344no—
208C23C2×C22⋊#59511yescharacteristic
209Q8—84no—
210Q8—684no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—41no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—172no—
220C2×C4—341no—
221C2×C4—341no—
222C2×C4—344no—
223C2×C4—341no—
224C2×C4—341no—
225C2×C4—341no—
226C2×C4—341no—
227C2×C4—341no—
228C2×C4—682no—
229C2×C4—682no—
230C2×C4—681no—
231C2×C4—681no—
232C2×C4#1058755111yescharacteristic
233C2×C4#1058755111yescharacteristic
234C2×C4#1058768012yes—
235C8—1362no—
236C8—1362no—
237C22—21no—
238C22—21no—
239C22#1176378411yescharacteristic
240C22C2×#1058755111yescharacteristic
241C22D17⋊#10111yescharacteristic
242C4—21no—
243C4—22no—
244C4—41no—
245C4—82no—
246C4—342no—
247C4—684no—
248C4—681no—
249C4—681no—
250C4—681no—
251C4#1176371912yes—
252C2—21no—
253C2—21no—
254C2#1454406411yescharacteristic
255C2#1454506311yescharacteristic
256C2C2×#1176371911yescharacteristic
subgroupG/H
centerC22C2×#10587551
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×C4⋊Q8C4
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4⋊Dic17C23
hypercenterC2×C4⋊Q8#595
hypocenterC17#11574
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
175. C17#11574semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145440462
#145440262
#145437272
#145339932
#1157417